Half adder circuit.

To understand what is a half adder you need to know what is an adder first. Adder circuit is a combinational digital circuit that is used for adding two numbers. A typical adder circuit produces a sum bit (denoted by S) and a carry bit (denoted by C) as the output. Typically adders are realized  for adding binary numbers but they can be also realized  for adding other formats like BCD (binary coded decimal, XS-3 etc. Besides addition, adder circuits can be used for a lot of other applications in digital electronics like address decoding, table index calculation etc. Adder circuits are of two types: Half adder ad Full adder. Full adder s have been already explained in a previous article and in this topic I am giving stress to half adders.

Half adder is a combinational  arithmetic circuit that adds two numbers and produces a sum bit (S) and carry bit (C) as the output. If  A and B are the input bits, then sum bit (S) is the X-OR of A and B  and the carry bit (C) will be the AND of A and B. From this it is clear that a half adder circuit can be easily constructed using one X-OR gate and one AND gate. Half adder is the simplest of all adder circuit, but it has a major disadvantage.  The half adder can add only two input bits (A and B) and has nothing to do with the carry if there is any in the input. So if the input to a half adder have a carry, then it will be neglected it and adds only the A and B bits. That means the binary addition process is not complete and that’s why it is called a half adder. The truth table, schematic representation and XOR//AND realization of a half adder are shown in the figure below.

half adder truth table
Truth table, schematic and realization of half adder

NAND gates or NOR gates can be used for realizing the half adder in universal logic and the relevant circuit diagrams are shown in the figure below.

Half adder using NOR gate
Half adder using NAND & NOR logic




  1. I thnink this is among the so much significant information for me.

    And i’m satisfied reading your article. But should commentary on few common things, The site style is wonderful, the articles is in point of fact nice : D.
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  2. k.vijayalakshmi

    can i have the logic diagram for half adder using nor gate only

  3. william masi

    useful information. thank u very much.

    • Sagar r n

      Bcoz combinational logic circuit is one which is solely depends upon the present state of the input. Not on the previous result. And even half adder also does not depend upon the previous results. I hope you’re clear now !!

    • Bcz it is combination of circuit like : And gate + exor gate like that perform half adder smiliary we can perform all arthmetic expersion using these gate using combining

    • hamza nadeem

      A combinational circuit that performs the addition of the two binary numbers is called the half adder. … The operation is performed by the logic circuit called half adder. The half adder produces two binary digit as output, a sum bit and the carry bit and accepts two binary digit as input.

  4. the half adder circuit with nor gates isnt giving the desired output